Indeterminacy and Truth Value Gaps
This chapter argues for the following theses. There are perfectly possible meanings (ones of a sort one would think are possessed by many vague predicates) which would necessitate a predicate's being gappy. Many arguments against the coherence of truth value gaps depend on a very narrow picture of saying, which ignores the possibility of such things as sui generis denial. Frege/Geach objections to things like sui generis denial dissolve once we observe that ‘not’ and other sentence compounding devices lead a double life, sometimes contributing to sense, sometimes to force. There is a simple compositional story about how (for instance) embedding a denial operator within a ‘force conditional’ makes if not A, then B fit to perform a sort of speech act which, when combined with B's denial, commits one to the aptness of asserting A. The trisection thesis — predicates trisect their domains into three groups, those they are true of, those they are false of, and the rest — is correct. The objection to the trisection thesis —that it is inconsistent with the idea that there are no sharp boundaries in a Sorites series — is not compelling: there is no conception of a ‘sharp boundary’ on which it's plausible, both that there are no sharp boundaries in a Sorites series, and that trisection involves the creation of sharp boundaries. Once we recognize that talk of indeterminacy is contrastive, we also recognize that higher order vagueness is not inconsistent with trisection. We also, once we think of indeterminacy as contrastive, come to see that indeterminacy itself is indeterminate: if it is indeterminate whether p, that indeterminacy itself is not something that is settled, but is itself indeterminate.
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